Simple Equations Notes & Questions | Class 6 Mathematics | Drishti OS

Simple Equations

What an equation is — two expressions with an equals sign that may be true for some value of the variable.
The solution (root) — the value that makes both sides equal.
To solve one-step equations using inverse operations (balance idea).
To translate simple word problems into equations and solve them.

Verbal: An equation states that two quantities are equal. A solution is the value of the variable that makes it true.

Symbolic: x + 7 = 12 is an equation; solution x = 5 because 5 + 7 = 12.

Balance model: Both pans equal — whatever you add/remove from one side, do the same to the other.

Type	Has = ?	Example
Expression	No	3y + 2
Equation	Yes	3y + 2 = 11

One-step equations:

Two-step (Class 6): 2x + 3 = 11 → subtract 3 → 2x = 8 → x = 4.

Check: Substitute back — 2(4) + 3 = 11 ✓.

Word problem: "Think of a number, add 9, get 20" → x + 9 = 20 → x = 11.

Solve 3y − 5 = 16 and verify.

Step 1 — Add 5 to both sides: 3y = 21
Step 2 — Divide both sides by 3: y = 7
Step 3 — Check: 3(7) − 5 = 21 − 5 = 16 ✓

Raju's age: Raju is 4 years older than twice his sister's age. Raju is 18. Find sister's age s. 2s + 4 = 18 → 2s = 14 → s = 7 years.

Mistake	Why it happens	Fix
Doing operation on one side only	Forgetting balance	Same operation on both sides
Sign error: x − 3 = 8 → x = 5	Adding instead of subtracting	Add 3 to both sides → x = 11
Skipping verification	Rushing	Substitute solution into original equation
Wrong translation: "added to 5" as 5 + x vs x + 5	Order confusion	Both equal, but read phrase carefully in context

Open the Practice tab for graded questions on Simple Equations.